Spread 1 cup sauce in a 9-by-13-inch baking dish. Depending on how much eggplant you have, arrange the eggplant all in the bottom of the dish OR only use half the eggplant. Cover the eggplant layer with sauce and mozzarella. If using two layers of eggplant, place the other layer of eggplant on top, and top with more sauce and mozzarella. Sprinkle the top with remaining 2 tablespoons Parmesan. Bake until sauce is bubbling and cheese is melted, 15 to 20 minutes. Let stand 5 minutes before serving.